High-order splitting integrators for nonlinear Schrödinger equations over long times

Abstract

The long-time behaviour of splitting integrators applied to nonlinear Schrödinger equations in a weakly nonlinear setting is studied. It is proven that the energy is nearly conserved on long time intervals. The analysis includes all consistent splitting integrators with real-valued coefficients, in particular splitting integrators of high order. The proof is based on a completely resonant modulated Fourier expansion in time of the numerical solution.